"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10

C
VIN
Figure 7–20. Lead-Lag Compensated Op Amp
A
K
1 s 1 2 s 1
R
RG
R G
R G R F
+
_ a
RF
VOUT
RCs 1
RR G RR F R G R F
R G R F
Voltage-Feedback Op Amp Compensation
Lead-Lag Compensation
Cs 1
(7–23)
Referring to Figure 7–21, a pole is introduced at ω = 1/RC, and this pole reduces the gain
3 dB at the breakpoint. When the zero occurs prior to the first op amp pole it cancels out
the phase shift caused by the ω = 1/RC pole. The phase shift is completely canceled before
the second op amp pole occurs, and the circuit reacts as if the pole was never
introduced. Nevertheless, Aβ is reduced by 3 dB or more, so the loop gain crosses the
0-dB axis at a lower frequency. The beauty of lead lag compensation is that the closedloop
ideal gain is not affected as is shown below. The Thevenin equivalent of the input
circuit is calculated in Equation 7–24, the circuit gain in terms of Thevenin equivalents is
calculated in Equation 7–25, and the ideal closed-loop gain is calculated in Equation
7–26.
20 Log (aRG/(RF + RG))
0dB
/
20 Log (Aβ)
Before Compensation
20 Log (Aβ)
After Compensation
Log(f)
1/(RC) 1/τ1 1/τ2
Compensation Network
(RRG + RFR + RFRG)
C
(RF + RG)
Figure 7–21. Bode Plot of Lead-Lag Compensated Op Amp
Amplitude
1
7-19